基于值域的稠密性和闭性,有界线性算子的点谱可进一步细分为互不相交的四个组成部分,即四类点谱.设H_1,H_2,H_3为无穷维复可分Hilbert空间,记M_(D,E,F)=(A D E0 B F0 0 C)∈B(H_1⊕H_2⊕H_3).当对角算子A,B,C固定时,给出了M_(D,E,F)的四类点谱随D,E,F扰动的完全描述.
According to the denseness and the closedness of range, the point spectrum of a bounded linear operator is split into four disjoint parts, i.e., four classes of point spectra. Let H1, H2, H3 be infinite dimensional complex separable Hilbert spaces, and write MD,E,F= (A D E0 B F0 0 C)∈B(H_1⊕H_2⊕H_3). Fixed the diagonal operators A ∈ B(H1), B ∈ B(H2), C ∈B(H3), the perturbation descriptions of various point spectra for MD,E,F are given when D, E, F run over B(H2, H1), B(H3, H1),B(H3, H2), respectively.